Toeplitz operators related to strongly singular Calderón-Zygmund operators

Abstract

In this paper, the boundedness of Toeplitz operator T b (f ) related to strongly singular Calderón-Zygmund operators and Lipschitz functionWe also obtain the boundedness of generalized Toeplitz operator Θ b α0 from L p (R n ) to L q (R n ), 1 q = 1 p − α0+β0 n . All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator T b (f ) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on L p (R n ), 1 < p < ∞ .

Weighted norm inequalities for Toeplitz type operators associated to generalized Calderón–Zygmund operators

“…(1976) proved that the commutators [ b ,  T ], which generated by Calderón–Zygmund singular integral operators and BMO functions, are bounded on for Chanillo (1982) obtained a similar result when Calderón–Zygmund singular integral operators are replaced by the fractional integral operators. Recently, some Toeplitz type operators associated to the singular integral operators are introduced, and the boundedness for the operators generated by singular integral operators and BMO functions and Lipschitz functions are obtained (see Lin and Lu 2006; Lu and Mo 2009). …”

Boundedness of Commutators on Hardy-Type Spaces

“…Denote 1/q 1 = 1/p 1 − β 0 /n. By Hölder's inequality and the (L p1 , L q1 ) boundedness of [b, T ]( [6]), the estimate of I can be established.…”

“…Recently, the authors in [6] have obtained the boundedness of the commutator [b, T ] generated by strongly singular Calderón-Zygmund operator T and a Lipschitz function b from L p (R n ) to L q (R n ). To be…”

$$M^k$$ M k -type sharp estimates and boundedness on Morrey space for Toeplitz type operators associated to fractional integral and singular integral operator with general kernel

“…In [1], some singular integral operators with general kernel are introduced, and the boundedness for the operators and their commutators generated by BMO and Lipschitz functions are obtained(see [1,9]). In [7,8], some Toeplitz type operators related to the singular integral operators and strongly singular integral operators are introduced, and the boundedness for the operators generated by BMO and Lipschitz functions are obtained. In this paper, we…”